Question:
Jennifer can finish a work in 6 days. Linda can finish the same work in 7 days while Elizabeth can finish the work in 8 days. How long will it take to finish it if they work together?
Correct Answer
2 22/73 days or 2.301 days
Solution And Explanation
Solution
Given,
The number of days required to finish a piece of work by Jennifer = 6 days
And, the number of days required to finish the same work by Linda = 7 days
And, the number of days required to finish the same work by Elizabeth = 8 days
Thus, the number of days required to finish the work by all of them if they work together = ?
Here,
∵ In 6 days the work is done by Jennifer = 1
∴ The work done by Jennifer in 1 day = 1/6
Similarly,
∵ In 7 days the work is done by Linda = 1
∴ The work done by Linda in 1 day = 1/7
Similarly,
∵ In 8 days the work is done by Elizabeth = 1
∴ The work done by Elizabeth in 1 day = 1/8 part
Now, the work done by Jennifer, Linda, and Elizabeth together in 1 day
= Jennifer's 1 day work + Linda's 1 day work + Elizabeth's 1 day work
= 1/6 + 1/7 + 1/8
= 28 + 24 + 21/168
= 73/168 part of work
This means in 1 day, 73/168 part of work is done by Jennifer, Linda and Elizabeth working together.
Now, the number of days required to finish 73/168 part of work by Jennifer, Linda, and Elizabeth working together = 1
∴ the number of days required to finish the whole work (1 work) by Jennifer + Linda + Elizabeth together
= 1/73/168
= 1 × 168/73 = 168/73 days
= 2 22/73 days = or 2.301 days
Thus, Jennifer, Linda, and Elizabeth working together will finish the total work (1 work) in 2 22/73 days = or 2.301 days Answer
Shortcut Trick to solve the problems based on time and work using formula
Case: If A can finish a work in a days, B can finish the same work in b days, and C can finish the work in c days
then working together the number of days required to finish the work
= a × b × c/ab + ac + bc days.
Here given,
The number of days required to finish the work by Jennifer = 6 days
And the number of days required to finish the same work by Linda = 7 days
And the number of days required to finish the work by Elizabeth = 8 days
Thus, the number of days required to finish the work by Jennifer, Linda, and Elizabeth together = ?
Here a = 6 days
And, b = 7 days
And, c = 8 days
Thus, using formula a × b × c/ab + ac + bc days
The number of days required to finish the work when Jennifer, Linda, and Elizabeth working together
= 6 × 7 × 8/6 × 7 + 6 × 8 + 7 × 8 days
= 336/42 + 48 + 56 days
= 336/146 days
= 336/146 days
= 336 ÷ 2/146 ÷ 2 = 168/73 days
= 2 22/73 days or 2.301
Thus, Jennifer, Linda, and Elizabeth together will finish the work in 2 22/73 days or 2.301 days Answer
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